Monotonic classification is a kind of special task in machine learning and pattern recognition. Monotonicity constraints between features and decision should be taken into account in these tasks. However, most existing techniques are not able to discover and represent the ordinal structures in monotonic datasets. Thus, they are inapplicable to monotonic classification. Feature selection has been proven effective in improving classification performance and avoiding overfitting. To the best of our knowledge, no technique has been specially designed to select features in monotonic classification until now. In this paper, we introduce a function, which is called rank mutual information, to evaluate monotonic consistency between features and decision in monotonic tasks. This function combines the advantages of dominance rough sets in reflecting ordinal structures and mutual information in terms of robustness. Then, rank mutual information is integrated with the search strategy of min-redundancy and max-relevance to compute optimal subsets of features. A collection of numerical experiments are given to show the effectiveness of the proposed technique.

Rough sets, especially fuzzy rough sets, are supposedly a powerful mathematical tool to deal with uncertainty in data analysis. This theory has been applied to feature selection, dimensionality reduction, and rule learning. However, it is pointed out that the classical model of fuzzy rough sets is sensitive to noisy information, which is considered as a main source of uncertainty in applications. This disadvantage limits the applicability of fuzzy rough sets. In this paper, we reveal why the classical fuzzy rough set model is sensitive to noise and how noisy samples impose influence on fuzzy rough computation. Based on this discussion, we study the properties of some current fuzzy rough models in dealing with noisy data and introduce several new robust models. The properties of the proposed models are also discussed. Finally, a robust classification algorithm is designed based on fuzzy lower approximations. Some numerical experiments are given to illustrate the effectiveness of the models. The classifiers that are developed with the proposed models achieve good generalization performance.

In many decision making tasks, values of features and decision are ordinal. Moreover, there is a monotonic constraint that the objects with better feature values should not be assigned to a worse decision class. Such problems are called ordinal classification with monotonicity constraint. Some learning algorithms have been developed to handle this kind of tasks in recent years. However, experiments show that these algorithms are sensitive to noisy samples and do not work well in real-world applications. In this work, we introduce a new measure of feature quality, called rank mutual information (RMI), which combines the advantage of robustness of Shannon's entropy with the ability of dominance rough sets in extracting ordinal structures from monotonic data sets. Then, we design a decision tree algorithm (REMT) based on rank mutual information. The theoretic and experimental analysis shows that the proposed algorithm can get monotonically consistent decision trees, if training samples are monotonically consistent. Its performance is still good when data are contaminated with noise.

A support vector machine (SVM) is a popular algorithm for classification learning. The classical SVM effectively manages classification tasks defined by means of numerical attributes. However, both numerical and nominal attributes are used in practical tasks and the classical SVM does not fully consider the difference between them. Nominal attributes are usually regarded as numerical after coding. This may deteriorate the performance of learning algorithms. In this study, we propose a novel SVM algorithm for learning with heterogeneous data, known as a heterogeneous SVM (HSVM). The proposed algorithm learns an mapping to embed nominal attributes into a real space by minimizing an estimated generalization error, instead of by direct coding. Extensive experiments are conducted, and some interesting results are obtained. The experiments show that HSVM improves classification performance for both nominal and heterogeneous data.

Heterogeneous feature representations are widely used in machine learning and pattern recognition, especially for multimedia analysis. The multi-modal, often also high- dimensional , features may contain redundant and irrelevant information that can deteriorate the performance of modeling in classification. It is a challenging problem to select the informative features for a given task from the redundant and heterogeneous feature groups. In this paper, we propose a novel framework to address this problem. This framework is composed of two modules, namely, multi-modal deep neural networks and feature selection with sparse group LASSO. Given diverse groups of discriminative features, the proposed technique first converts the multi-modal data into a unified representation with different branches of the multi-modal deep neural networks. Then, through solving a sparse group LASSO problem, the feature selection component is used to derive a weight vector to indicate the importance of the feature groups. Finally, the feature groups with large weights are considered more relevant and hence are selected. We evaluate our framework on three image classification datasets. Experimental results show that the proposed approach is effective in selecting the relevant feature groups and achieves competitive classification performance as compared with several recent baseline methods.